An Extensible Framework for Probabilistic Search of Stochastically-moving Targets Characterized by Generalized Gaussian Distributions or Experimentally-defined Regions of Interest

Abstract: This paper presents a continuous-time framework for modeling the evolution of a probability density function (PDF) summarizing the region of interest (ROI) during the search for a stochastically-moving, statistically stationary target. This framework utilizes a Fokker-Planck partial differential equation representing the evolution of this PDF subject to: diffusion modeling the spread of the PDF due to the random motion of the target, advection modeling the relaxation of the PDF back to a specified steady profile summarizing the ROI in the absence of observations, and observations substantially reducing the PDF within the vicinity of the search vehicles patrolling the ROI. As a medium for testing the proposed search algorithm, this work defines a new, more general formulation for the multivariate Generalized Gaussian Distribution (GGD), an extension of the Gaussian Distribution described by shaping parameter beta. Additionally, we define a formulation with enhanced flexibility, the Generalized Gaussian Distribution with Anisotropic Flatness (GGDAF). Two techniques are explored that convert a set of target location observations into a steady-state PDF summarizing the ROI of the target, wherein the steady-state advection is numerically solved for. This work thus provides a novel framework for the probabilistic search of stochastically-moving targets, accommodating both non-evasive and evasive behavior.

Recommended citation: B. L. Hanson, M. Zhao, T. R. Bewley "An Extensible Framework for Probabilistic Search of Stochastically-moving Targets Characterized by Generalized Gaussian Distributions or Experimentally-defined Regions of Interest," Submitted to Communications in Statistics - Theory and Methods, 2024.